How do you fix a washing machine drain that overflows

Is it only during the rinse cycle and not the wash cycle?

I would think that the drain is plugged. If there's a trap on the drain, open that and see if the plug is in there. A "snake" can also be used to remove the clog. Home centers rent power snakes, and you can buy a cheap hand-powered one. Sometimes a plunger will work if you can get a seal around the drain.

I agree with rwnterton assuming that this is a new problem and you are sure the drain pipe has the basic capacity to handle all the rinse water.